Sketch, on the same diagram, the curves with equations $y = \left| \frac{x+1}{x-2} \right|$ and \(

Question

Sketch, on the same diagram, the curves with equations $y = \left| \frac{x+1}{x-2} \right|$ and $y = \ln \left( 1 - \frac{x}{2} \right) + \frac{1}{2}$, stating the equations of any asymptotes and the coordinates of any points of intersection with the axes. Label the two curves clearly.[5] Hence solve the inequality $\left| \frac{x+1}{x-2} \right| \ge \ln \left( 1 - \frac{x}{2} \right) + \frac{1}{2}$.[1]

Accepted Answer

(a) Modulus curve: intercepts $(-1,0),(0,\frac{1}{2})$, asymptotes $x=2,y=1$. Logarithmic curve: intercepts $(0,\frac{1}{2}),(2(1-\mathrm e^{-\frac{1}{2}}),0)$, asymptote $x=2$, domain $x<2$. (b) $0\le x<2$.

2023 EJC Promo Q3

2023 EJC Promo Q3

Solution:

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